Social influence is among the main driving mechanisms of many collective phenomena in society, including the spreading of innovations, ideas, fads, or social movements. Many of these processes have been modelled either as simple contagion (like the Bass model of innovation diffusion), or as complex contagion (like the Watts model of adoption cascades). In these models social influence is commonly assumed to be homogeneous across ties in the network, while in reality relationships may constitute entirely different dyadic types, modelled as distinct layers in a multiplex network. We address this challenge by studying a dynamical cascade model on multiplex networks, where edge features capture diversity in social influence. We focus on a two-layer multiplex networks, such that spreading is determined by the adoption threshold of nodes and the average degree of each layer in the multiplex. By varying edge overlap between layers, we find that the presence of multiple layers induces unexpected dynamical behaviour, either speeding up or slowing down contagion relative to the simplex case, depending on the adoption threshold and overlap of links in each layer. Further, we observe the emergence of dual cascading regimes, where avalanches of behavioural change are induced by individual layers in the multiplex, emerging as pairs of first and second order phase transitions. We explore this surprising behaviour using simulations, and an analytic formalism accurately capturing the effects of layer heterogeneity and link overlap, building upon the work in. These results may help in developing more accurate spreading models of real behavioural cascades on multilayer social networks
